Hello,
Can we state that the existence of non-trivial languages in NP\NPC is an open problem in CS without proving it, or do we have to show that we can't prove it without determining whether P=NP or P!=NP?

If P=NP then of course there are no NP-intermediate problems.
Otherwise, it is a fact (which we don't prove) that there are indeed NP-intermediate problems. You can use this fact, although I don't see why you would need to.